Multifractality and long memory of a financial index

TL;DR

This study investigates the multifractal nature and long memory effects in high-frequency returns of Madrid's IBEX35 index, revealing endogenous long-range dependencies likely influencing typical financial time series behaviors.

Contribution

It demonstrates the multifractality of the IBEX35 index and attributes it to long memory effects, distinguishing between high-frequency and slowly-varying endogenous components.

Findings

Index exhibits a wide singularity spectrum indicating multifractality.

Long memory is due to a superposition of high-frequency and slow-varying components.

Slow component is endogenous and may explain stylized facts in financial data.

Abstract

In this paper we will try to assess the multifractality displayed by the high-frequency returns of Madrid's Stock Exchange IBEX35 index. A Multifractal Detrended Fluctuation Analysis shows that this index has a wide singularity spectrum which is most likely caused by its long memory. Our findings also show that this long-memory can be considered as the superposition of a high-frequency component (related to the daily cycles of arrival of information to the market), over a slowly-varying component that reverberates for long periods of time and which shows no apparent relation with human economic cycles. This later component is therefore postulated to be endogenous to market's dynamics and to be also the most probable source of some of the stylized facts commonly associated with financial time series.